It depends but if you are a MA resident and you won a contest without actually being in CA, then this prize money is not be considered CA sourced.
Therefore, you would only need to file a nonresident CA state income tax return if you wanted a full refund of any CA withholdings. You would still report the prize winnings on both your federal and MA resident state income tax returns and you would report the full amount of the prize (before any CA withholdings were taken out).
When you are entering the 1099-MISC information into TurboTax, just make sure that you do not relate it to any work-type income and you will get a landing screen that will ask what the 1099-MISC relates to. Just select "prize winnings" (see screenshot) and the amount will be reported on line 21 of your 1040 and will not be subject to any self-employment taxes.
